Bank cashier mistake puzzle
You went to a bank to cash out your cheque.
By mistake the bank cashier gives you-
- Dollar amount in cent, and
- Cent amount in dollars.
On the way home you spends 5 cent, and then suddenly you notices that you have twice the amount of your cheque.
How much was have you written on cheque ?
The answer is 31$ and 63 cents
Method : Lets assume Cent = z and $ = 100z , no. of dollars =x and no.of cents = y
So,Initially he had 100zx + zy
Now after cashier’s mistake it becomes 100zy + zx
After spending 5 cents it becomes double
So now equation is 100zy + zx -5z = 200zx + 2zy
or 199x = 98y -5
Now,value of y cannot be greater than 100 (otherwise it becomes $)
so plotting values of y for 1 to 100,we get only 1 integer value for x i.e. 31 for y = 63
Hence the answer 31$ and 63 cents
Enjoy!
Answer: 31.63 $
Let the amount in cents be x, and amount in dollars be y
1. x>y (otherwise the second number would be smaller)
2. Amount of cents in second number is y, since y-5<x, there must be 1 dollar carried forward when doubling.
3. Amount of dollars in second number is x, hence (x-1)/2=y (take away the 1 dollar carried forward then half)
4. y can also be expressed as y=2x-100+5 (double x and take away the 100 cents carried forward, then add the 5 cents)
5. Therefore (x-1)/2=2x-100+5
6. Solving the expression above gives x=63, and y=(x-1)/2=31
Hope all is clear:)
Your Answer
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